CoCalc -- 11.1 Participation Aiuka N.ipynb

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ubuntu2004

Kernel: Python 3 (system-wide)

In this assignment we will use Bisection Method to find a root of the function $f(x) = ln(x)-sin(x)$ in the interval (2, 4) with an error bound of 0.001.

In [3]:

def bisection(a,b,f,err): #Our bisection function.
    c = (a+b)/2
    while c - a > err:
        if f(c) == 0:
            return c
        elif f(a)*f(c) > 0:
            a = c
        else:
            b = c
        c = (a+b)/2
    return c

In [4]:

import numpy as np
import matplotlib.pyplot as plt #import libs
def p(x):
    return np.log(x)-np.sin(x) #We use np.log(x) from NumPy to find ln(x).

In [5]:

bisection(2,4,p,0.001) #Our root is at approximately ~2.2197265625

Out[5]:

2.2197265625

In [6]:

p(2.2197265625)

Out[6]:

0.0006532685362758972

In [7]:

x = np.linspace(1,10,1000)
y = np.log(x)-np.sin(x)
plt.plot(x,y)

Out[7]:

[<matplotlib.lines.Line2D at 0x7f4c7d2ea8e0>]

On this plot we can assume that the roots of the function f(x)=ln(x)-sin(x) are not located on (2, 4) interval.

In [0]:

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